Expert Answer to "There are functions for which it is possible..." - Plainmath

landdenaw

Answered question

2022-06-13

There are functions for which it is possible for only one of these to be true.
give an example of such a function

Answer & Explanation

hildiadau0o

Beginner2022-06-14Added 21 answers

Consider

f : R \to R

given by

f (x) = x + 1

for

x \geq 0

and

f (x) = x - 1

for

x < 0

Now consider

g : R \to R

given by

g (x) = x - 1

for

x \in [1, \infty)

,

g (x) = x + 1

for

x \in (- \infty, - 1)

and

g (x) = 1

otherwise.
Then

(g \circ f) (x) = x

for all

x \in R

but

(f \circ g) (0) = f (1) = 2

.

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